Convert 160 481 517 728 110 to a Signed Binary in Two's (2's) Complement Representation

How to convert decimal number 160 481 517 728 110(10) to a signed binary in two's (2's) complement representation

What are the steps to convert decimal number
160 481 517 728 110 to a signed binary in two's (2's) complement representation?

  • A signed integer, written in base ten, or a decimal system number, is a number written using the digits 0 through 9 and the sign, which can be positive (+) or negative (-). If positive, the sign is usually not written. A number written in base two, or binary, is a number written using only the digits 0 and 1.

1. Divide the number repeatedly by 2:

Keep track of each remainder.

We stop when we get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 160 481 517 728 110 ÷ 2 = 80 240 758 864 055 + 0;
  • 80 240 758 864 055 ÷ 2 = 40 120 379 432 027 + 1;
  • 40 120 379 432 027 ÷ 2 = 20 060 189 716 013 + 1;
  • 20 060 189 716 013 ÷ 2 = 10 030 094 858 006 + 1;
  • 10 030 094 858 006 ÷ 2 = 5 015 047 429 003 + 0;
  • 5 015 047 429 003 ÷ 2 = 2 507 523 714 501 + 1;
  • 2 507 523 714 501 ÷ 2 = 1 253 761 857 250 + 1;
  • 1 253 761 857 250 ÷ 2 = 626 880 928 625 + 0;
  • 626 880 928 625 ÷ 2 = 313 440 464 312 + 1;
  • 313 440 464 312 ÷ 2 = 156 720 232 156 + 0;
  • 156 720 232 156 ÷ 2 = 78 360 116 078 + 0;
  • 78 360 116 078 ÷ 2 = 39 180 058 039 + 0;
  • 39 180 058 039 ÷ 2 = 19 590 029 019 + 1;
  • 19 590 029 019 ÷ 2 = 9 795 014 509 + 1;
  • 9 795 014 509 ÷ 2 = 4 897 507 254 + 1;
  • 4 897 507 254 ÷ 2 = 2 448 753 627 + 0;
  • 2 448 753 627 ÷ 2 = 1 224 376 813 + 1;
  • 1 224 376 813 ÷ 2 = 612 188 406 + 1;
  • 612 188 406 ÷ 2 = 306 094 203 + 0;
  • 306 094 203 ÷ 2 = 153 047 101 + 1;
  • 153 047 101 ÷ 2 = 76 523 550 + 1;
  • 76 523 550 ÷ 2 = 38 261 775 + 0;
  • 38 261 775 ÷ 2 = 19 130 887 + 1;
  • 19 130 887 ÷ 2 = 9 565 443 + 1;
  • 9 565 443 ÷ 2 = 4 782 721 + 1;
  • 4 782 721 ÷ 2 = 2 391 360 + 1;
  • 2 391 360 ÷ 2 = 1 195 680 + 0;
  • 1 195 680 ÷ 2 = 597 840 + 0;
  • 597 840 ÷ 2 = 298 920 + 0;
  • 298 920 ÷ 2 = 149 460 + 0;
  • 149 460 ÷ 2 = 74 730 + 0;
  • 74 730 ÷ 2 = 37 365 + 0;
  • 37 365 ÷ 2 = 18 682 + 1;
  • 18 682 ÷ 2 = 9 341 + 0;
  • 9 341 ÷ 2 = 4 670 + 1;
  • 4 670 ÷ 2 = 2 335 + 0;
  • 2 335 ÷ 2 = 1 167 + 1;
  • 1 167 ÷ 2 = 583 + 1;
  • 583 ÷ 2 = 291 + 1;
  • 291 ÷ 2 = 145 + 1;
  • 145 ÷ 2 = 72 + 1;
  • 72 ÷ 2 = 36 + 0;
  • 36 ÷ 2 = 18 + 0;
  • 18 ÷ 2 = 9 + 0;
  • 9 ÷ 2 = 4 + 1;
  • 4 ÷ 2 = 2 + 0;
  • 2 ÷ 2 = 1 + 0;
  • 1 ÷ 2 = 0 + 1;

2. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.

160 481 517 728 110(10) = 1001 0001 1111 0101 0000 0011 1101 1011 0111 0001 0110 1110(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 48.

  • A signed binary's bit length must be equal to a power of 2, as of:
  • 21 = 2; 22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 64; ...
  • The first bit (the leftmost) indicates the sign:
  • 0 = positive integer number, 1 = negative integer number

The least number that is:

1) a power of 2

2) and is larger than the actual length, 48,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)

=== is: 64.


4. Get the positive binary computer representation on 64 bits (8 Bytes):

If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64.


Decimal Number 160 481 517 728 110(10) converted to signed binary in two's complement representation:

160 481 517 728 110(10) = 0000 0000 0000 0000 1001 0001 1111 0101 0000 0011 1101 1011 0111 0001 0110 1110

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

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How to convert signed integers from decimal system to signed binary in two's complement representation

Follow the steps below to convert a signed base 10 integer number to signed binary in two's complement representation:

  • 1. If the number to be converted is negative, start with the positive version of the number.
  • 2. Divide repeatedly by 2 the positive representation of the integer number, keeping track of each remainder, until we get a quotient that is zero.
  • 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above. Thus, the last remainder of the divisions becomes the first symbol (the leftmost) of the base two number, while the first remainder becomes the last symbol (the rightmost).
  • 4. Binary numbers represented in computer language must have 4, 8, 16, 32, 64, ... bit length (a power of 2) - if needed, add extra bits on 0 in front (to the left) of the base 2 number above, up to the required length, so that the first bit (the leftmost) will be 0, correctly representing a positive number.
  • 5. To get the negative integer number representation in signed binary one's complement, replace all 0 bits with 1s and all 1 bits with 0s (reversing the digits).
  • 6. To get the negative integer number, in signed binary two's complement representation, add 1 to the number above.

Example: convert the negative number -60 from the decimal system (base ten) to signed binary in two's complement:

  • 1. Start with the positive version of the number: |-60| = 60
  • 2. Divide repeatedly 60 by 2, keeping track of each remainder:
    • division = quotient + remainder
    • 60 ÷ 2 = 30 + 0
    • 30 ÷ 2 = 15 + 0
    • 15 ÷ 2 = 7 + 1
    • 7 ÷ 2 = 3 + 1
    • 3 ÷ 2 = 1 + 1
    • 1 ÷ 2 = 0 + 1
  • 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above:
    60(10) = 11 1100(2)
  • 4. Bit length of base 2 representation number is 6, so the positive binary computer representation of a signed binary will take in this particular case 8 bits (the least power of 2 larger than 6) - add extra 0 digits in front of the base 2 number, up to the required length:
    60(10) = 0011 1100(2)
  • 5. To get the negative integer number representation in signed binary one's complement, replace all the 0 bits with 1s and all 1 bits with 0s (reversing the digits):
    !(0011 1100) = 1100 0011
  • 6. To get the negative integer number, signed binary in two's complement representation, add 1 to the number above:
    -60(10) = 1100 0011 + 1 = 1100 0100
  • Number -60(10), signed integer, converted from decimal system (base 10) to signed binary two's complement representation = 1100 0100